PCA
# with scaling
pr.out=prcomp(USArrests, scale=TRUE)
names(pr.out)
## [1] "sdev" "rotation" "center" "scale" "x"
# the centering and scaling used (means)
pr.out$center
## Murder Assault UrbanPop Rape
## 7.788 170.760 65.540 21.232
# the matrix of variable loadings (eigenvectors)
pr.out$scale
## Murder Assault UrbanPop Rape
## 4.355510 83.337661 14.474763 9.366385
pr.out$rotation
## PC1 PC2 PC3 PC4
## Murder -0.5358995 0.4181809 -0.3412327 0.64922780
## Assault -0.5831836 0.1879856 -0.2681484 -0.74340748
## UrbanPop -0.2781909 -0.8728062 -0.3780158 0.13387773
## Rape -0.5434321 -0.1673186 0.8177779 0.08902432
dim(pr.out$x)
## [1] 50 4
pr.out$rotation=-pr.out$rotation
pr.out$x=-pr.out$x
biplot(pr.out, scale=0)
pr.out$sdev
## [1] 1.5748783 0.9948694 0.5971291 0.4164494
pr.var=pr.out$sdev^2
pr.var
## [1] 2.4802416 0.9897652 0.3565632 0.1734301
pve=pr.var/sum(pr.var)
pve
## [1] 0.62006039 0.24744129 0.08914080 0.04335752
plot(pve, xlab="Principal Component", ylab="Proportion of Variance Explained", ylim=c(0,1),type='b')
plot(cumsum(pve), xlab="Principal Component", ylab="Cumulative Proportion of Variance Explained", ylim=c(0,1),type='b')
## Use factoextra package
library(factoextra)
## Loading required package: ggplot2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
fviz(pr.out, "ind", geom = "auto", mean.point = TRUE, font.family = "Georgia")
fviz_pca_biplot(pr.out, font.family = "Georgia", col.var="firebrick1")
K-Means Clustering
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(ggplot2)
library(RColorBrewer)
computers = read.csv("https://raw.githubusercontent.com/guru99-edu/R-Programming/master/computers.csv")
# Only retain two variables for illustration
rescaled_comp <- computers[4:5] %>%
mutate(hd_scal = scale(hd),
ram_scal = scale(ram)) %>%
select(c(hd_scal, ram_scal))
ggplot(data = rescaled_comp, aes(x = hd_scal, y = ram_scal)) +
geom_point(pch=20, col = "blue") + theme_bw() +
labs(x = "Hard drive size (Scaled)", y ="RAM size (Scaled)" ) +
theme(text = element_text(family="Georgia"))
library(animation)
set.seed(2345)
library(animation)
# Animate the K-mean clustering process, cluster no. = 4
kmeans.ani(rescaled_comp[1:2], centers = 4, pch = 15:18, col = 1:4)
## Iris example
# Without grouping by species
ggplot(iris, aes(Petal.Length, Petal.Width)) + geom_point() +
theme_bw() +
scale_color_manual(values=c("firebrick1","forestgreen","darkblue"))
# With grouping by species
ggplot(iris, aes(Petal.Length, Petal.Width, color = Species)) + geom_point() +
theme_bw() +
scale_color_manual(values=c("firebrick1","forestgreen","darkblue"))
# Check k-means clusters
## Starting with three clusters and 20 initial configurations
set.seed(20)
irisCluster <- kmeans(iris[, 3:4], 3, nstart = 20)
irisCluster
## K-means clustering with 3 clusters of sizes 52, 48, 50
##
## Cluster means:
## Petal.Length Petal.Width
## 1 4.269231 1.342308
## 2 5.595833 2.037500
## 3 1.462000 0.246000
##
## Clustering vector:
## [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [38] 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 2 2 2
## [112] 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
## [149] 2 2
##
## Within cluster sum of squares by cluster:
## [1] 13.05769 16.29167 2.02200
## (between_SS / total_SS = 94.3 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
class(irisCluster$cluster)
## [1] "integer"
# Confusion matrix
table(irisCluster$cluster, iris$Species)
##
## setosa versicolor virginica
## 1 0 48 4
## 2 0 2 46
## 3 50 0 0
irisCluster$cluster <- as.factor(irisCluster$cluster)
ggplot(iris, aes(Petal.Length, Petal.Width, color = irisCluster$cluster)) + geom_point() +
scale_color_manual(values=c("firebrick1","forestgreen","darkblue")) +
theme_bw()
actual = ggplot(iris, aes(Petal.Length, Petal.Width, color = Species)) + geom_point() +
theme_bw() +
scale_color_manual(values=c("firebrick1","forestgreen","darkblue")) +
theme(legend.position="bottom") +
theme(text = element_text(family="Georgia"))
kmc = ggplot(iris, aes(Petal.Length, Petal.Width, color = irisCluster$cluster)) + geom_point() +
theme_bw() +
scale_color_manual(values=c("firebrick1", "darkblue", "forestgreen")) +
theme(legend.position="bottom") +
theme(text = element_text(family="Georgia"))
library(grid)
library(gridExtra)
##
## Attaching package: 'gridExtra'
## The following object is masked from 'package:dplyr':
##
## combine
grid.arrange(arrangeGrob(actual, kmc, ncol=2, widths=c(1,1)), nrow=1)
# Wine example
library(rattle.data)
data(wine, package="rattle.data")
## Choose and scale variables
wine_subset <- scale(wine[ , c(2:4)])
## Create cluster using k-means, k = 3, with 25 initial configurations
wine_cluster <- kmeans(wine_subset, centers = 3,
iter.max = 10,
nstart = 25)
wine_cluster
## K-means clustering with 3 clusters of sizes 48, 60, 70
##
## Cluster means:
## Alcohol Malic Ash
## 1 0.1470536 1.3907328 0.2534220
## 2 0.8914655 -0.4522073 0.5406223
## 3 -0.8649501 -0.5660390 -0.6371656
##
## Clustering vector:
## [1] 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2
## [38] 2 3 1 2 1 2 1 3 1 1 2 2 2 3 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 2 3 3 2 2 2
## [75] 3 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [112] 3 1 3 3 3 3 3 1 3 3 2 1 1 1 3 3 3 3 1 3 1 3 1 3 3 1 1 1 1 1 2 1 1 1 1 1 1
## [149] 1 1 1 1 2 1 3 1 1 1 2 2 1 1 1 1 2 1 1 1 2 1 3 3 2 1 1 1 2 1
##
## Within cluster sum of squares by cluster:
## [1] 73.71460 67.98619 111.63512
## (between_SS / total_SS = 52.3 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
# Create a function to compute and plot total within-cluster sum of square (withinss)
wssplot <- function(data, nc=15, seed=1234){
wss <- (nrow(data)-1)*sum(apply(data,2,var))
for (i in 2:nc){
set.seed(seed)
wss[i] <- sum(kmeans(data, centers=i)$withinss)}
plot(1:nc, wss, type="b", xlab="Number of Clusters",
ylab="Within groups sum of squares")
}
# plotting values for each cluster starting from 1 to 9
wssplot(wine_subset, nc = 9)
# Plot results by dimensions
wine_cluster$cluster = as.factor(wine_cluster$cluster)
pairs(wine[2:4],
col = c("firebrick1", "darkblue", "forestgreen")[wine_cluster$cluster],
pch = c(15:17)[wine_cluster$cluster],
main = "K-Means Clusters: Wine data")
table(wine_cluster$cluster)
##
## 1 2 3
## 48 60 70
## Use the factoextra package to do more
# install.packages("factoextra")
library(factoextra)
fviz_nbclust(wine_subset, kmeans, method = "wss")
# Use eclust() procedure to do K-Means
wine.km <- eclust(wine_subset, "kmeans", nboot = 2)
# Print result
wine.km
## K-means clustering with 3 clusters of sizes 60, 70, 48
##
## Cluster means:
## Alcohol Malic Ash
## 1 0.8914655 -0.4522073 0.5406223
## 2 -0.8649501 -0.5660390 -0.6371656
## 3 0.1470536 1.3907328 0.2534220
##
## Clustering vector:
## [1] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [38] 1 2 3 1 3 1 3 2 3 3 1 1 1 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 2 2 1 1 1
## [75] 2 2 2 2 2 3 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [112] 2 3 2 2 2 2 2 3 2 2 1 3 3 3 2 2 2 2 3 2 3 2 3 2 2 3 3 3 3 3 1 3 3 3 3 3 3
## [149] 3 3 3 3 1 3 2 3 3 3 1 1 3 3 3 3 1 3 3 3 1 3 2 2 1 3 3 3 1 3
##
## Within cluster sum of squares by cluster:
## [1] 67.98619 111.63512 73.71460
## (between_SS / total_SS = 52.3 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault" "clust_plot"
## [11] "silinfo" "nbclust" "data" "gap_stat"
# Optimal number of clusters using gap statistics
wine.km$nbclust
## [1] 3
fviz_nbclust(wine_subset, kmeans, method = "gap_stat")
# Silhouette plot
fviz_silhouette(wine.km)
## cluster size ave.sil.width
## 1 1 60 0.44
## 2 2 70 0.33
## 3 3 48 0.30
fviz_cluster(wine_cluster, data = wine_subset) +
theme_bw() +
theme(text = element_text(family="Georgia"))
fviz_cluster(wine_cluster, data = wine_subset, ellipse.type = "norm") +
theme_bw() +
theme(text = element_text(family="Georgia"))
